Answer:
4x + 1
Step-by-step explanation:
24x² - 30x - 9 ( factor out 3 from each term )
= 3(8x² - 10x - 3) ← factor the quadratic
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 8 × - 3 = - 24 and sum = - 10
the factors are + 2 and - 12
use these factors to split the x- term
8x² + 2x - 12x - 3 ( factor the first/second and third/fourth terms )
= 2x(4x + 1) - 3(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(2x - 3)
then
24x² - 30x - 9 = 3(4x + 1)(2x - 3) ← in factored form
so (4x + 1) is a factor of the expression
